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Fine-grained 3D shape retrieval aims to retrieve 3D shapes similar to a query shape in a repository with models belonging to the same class, which requires shape descriptors to be capable of representing detailed geometric information to discriminate shapes with globally similar structures. Moreover, 3D objects can be placed with arbitrary position and orientation in real-world applications, which further requires shape descriptors to be robust to rigid transformations. The shape descriptions used in existing 3D shape retrieval systems fail to meet the above two criteria. In this paper, we introduce a novel deep architecture, RISA-Net, which learns rotation invariant 3D shape descriptors that are capable of encoding fine-grained geometric information and structural information, and thus achieve accurate results on the task of fine-grained 3D object retrieval. RISA-Net extracts a set of compact and detailed geometric features part-wisely and discriminatively estimates the contribution of each semantic part to shape representation. Furthermore, our method is able to learn the importance of geometric and structural information of all the parts when generating the final compact latent feature of a 3D shape for fine-grained retrieval. We also build and publish a new 3D shape dataset with sub-class labels for validating the performance of fine-grained 3D shape retrieval methods. Qualitative and quantitative experiments show that our RISA-Net outperforms state-of-the-art methods on the fine-grained object retrieval task, demonstrating its capability in geometric detail extraction. The code and dataset are available at: https://github.com/IGLICT/RisaNET.